A subgroup H of a group G is called power if there exists non-negative integer m such that = ⟨gm : g ∈ G⟩. Any which not nonpower G. Zhou, Shi and Duan, in 2006 paper, asked whether for every k (k ≥ 3), exist groups possessing exactly subgroups. We answer this question the affirmative by giving an explicit construction leads to at least one with subgroups, all 3, in_nitely many when composite g...

Let m be a natural number. It is proved that the simple groups G2(q) where q = 32m+1 and m ≥ 1,is uniquely determined by the set of orders of its maximal abelian subgroups. Mathematics Subject Classification: 20D05, 20D08

This paper, deals with some equivalence relations in fuzzy subgroups. Further the probability of commuting two fuzzy subgroups of some finite abelian groups is defined.

Valuations on a field K are encoded in the absolute Galois group GK of K: They are in one-to-one correspondence to the conjugacy classes of decomposition subgroups of GK which (apart from few exceptions) can be characterized in group theoretic terms. Roughly speaking decomposition subgroups of GK are maximal subgroups of GK with a Sylow-subgroup containing a non-trivial abelian normal subgroup....

We decompose the maximal ideal spectrum of the Hochschild cohomology ring of a block of a finite group into a disjoint union of subvarieties corresponding to elementary abelian p-subgroups of a defect group. These subvarieties are described in terms of group cohomological varieties and the Alperin-Broué correspondence on blocks. Our description leads in particular to a homeomorphism between the...

A presentation is obtained for the Chern subring modulo nilradical of both extraspecial p-groups of order p5, for p an odd prime. Moreover, it is proved that, for every extraspecial p-group of exponent p, the top Chern classes of the irreducible representations do not generate the Chern subring modulo nilradical. Finally, a related question about symplectic invariants is discussed, and solved f...

in this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite hamiltonian group. the coverings with three proper subgroups and the principal series of such a group are also counted. finally, we give a complete description of the lattice of characteristic subgroups of a finite h...